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arXiv · 2310.09954

Maximal Brill--Noether loci via the gonality stratification

Asher Auel·Richard Haburcak·Hannah Larson
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Abstract

We study the restriction of Brill-Noether loci to the gonality stratification of the moduli space of curves of fixed genus. As an application, we give new proofs that Brill-Noether loci with $\rho=-1$ have distinct support, and for fixed $r$ give lower bounds on when one direction of the non-containments of the Maximal Brill-Noether Loci Conjecture hold for Brill-Noether loci of rank $r$ linear systems. Using these techniques, we also show that Brill-Noether loci corresponding to rank $2$ linear systems are maximal as soon as $g\ge 28$ and prove the Maximal Brill-Noether Loci Conjecture for $g=20$.

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Asher Auel, Richard Haburcak, Hannah Larson. 2023-10-15. Maximal Brill--Noether loci via the gonality stratification. https://arxiv.org/abs/2310.09954

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